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trilinear correspondence there are two neutral pairs A,”, 4,”, which 
form a group with any point A,. The line A,”4,” is therefore a 
singular chord. 
One of the conics 4? consists of this chord and the line in 8 
resting on it and on a,. From this follows, that the locus of the 
À* which pass through A,” and A,", is a cubic dimonoid, containing a. 
The conical points of the six dimonoids can be indicated by 
Ar, "A,, Ay", "A,, A,", "A,; in this order the six neutral chords are 
each time defined by two successive symbols. They form a hexagon, 
inscribed in @,, a,, ds. 
To the singular chords belong apparently also the three lines 
9:2, and the three lines A;* A;* in g. 
Also the three lines a; are singular. For each plane through a, 
contains the conic determined by the intersections with a, and a, 
Let us consider the intersection of the surface %,, formed by these 
conics, with the plane 8. To this belongs the conic 3’; the rest 
consists of straight lines. On a, rest two lines g,,; their intersections 
with 8 determine together with the point A,* two straight lines 
belonging to WU, 
The line A,* A,* is cut by a line A, A, of the scroll correspond- 
ing to A,*; it lies} therefore on 2,, as well as the line 4,* A,*. 
Each of the three lines g,,, forms a pair of lines with a straight 
line in 8 through A,*. The intersection of AU, with 8 is therefore 
of order nie. 
The locus of the conics 47 which intersect a, twice, is accordingly 
a surface U? with a sevenfold line a,, containing the lines a,, a, 
and the conic p’. 
5. SINGULAR POINTS. All points Ax of the lines aj are singular. 
A straight line £ through a point A, is intersected by two lines 
ss is therefore a chord of two # passing through A. The planes of 
the 4* through A, envelop consequently a quadratic cone; from this 
follows, that through any point of 3’ two of these, 4? pass. Hence 
the locus of the 2? through A, is a surface (A‚)* with double curve 
g* and conical point A, 
Also the points B of 8° are singular. Through two points B, b’ 
2. hence Pp? counts three times in the locus ® of the 2? 
pass three 4 
through ZB. Moreover 6 and B have in common the three lines 
through B meeting the lines g,,,, and the lines joining B and the 
points Az*, which have to be counted twice. We conclude from this, 
that B is a surface of order fifteen with threefold curve # and 
three nodal lines aj; the point B is twelvefold. 
